International Portfolio Diversification and the Structure of GlobalProduction

Joseph B. SteinbergUniversity of Toronto, Department of Economics, 150 St. George Street, Toronto, M5S 3G7, Canada

Abstract

In recent decades, country portfolio home bias has fallen in advanced economies but not in emerg-ing economies. I use a dynamic general equilibrium model to show that changes in the distributionof global production and absorption explain this pattern. For advanced economies, whose share ofworld output fell as their trade openness rose, the model predicts an unambiguous drop in homebias. By contrast, emerging economies’ growth in both size and trade openness have opposing im-plications for portfolios. To quantify these forces I calibrate the model to real and counterfactualinput-output tables. Jointly, changes in the global production structure account for much of thedecline in home bias in advanced economies and lack thereof in emerging economies. Countrysize and trade openness account for most of this effect. Consistent with theory, the increase in theintermediate share of trade had little impact.

Keywords: country portfolios, international portfolio diversification, production structureJEL: F36, F41

1. Introduction

Since the 1990s, advanced economies’ country portfolios have shifted towards foreign assetswhile emerging economies’ portfolios have not. Concurrently, the structure of global productionand absorption has changed in several key ways: emerging economies have grown relative toadvanced economies, openness to international trade has risen, and trade consists increasingly ofintermediate inputs instead of final goods. In this paper, I use theory and quantitative analysisto show that changes in the global production structure explain trends in international portfoliodiversification.

Figure 1 depicts the stylized facts that motivate this study. Figure 1a shows that the meanlevel of international portfolio diversification, measured as the fraction of national wealth held inforeign assets, has risen dramatically in the United States and other advanced economies since the1990s but has changed little in emerging economies and the rest of the world. Recent studies byCoeurdacier and Rey (2013) and Mukherjee (2015) have documented similar trends. Figures 1b,

Email address: joseph.steinberg@utoronto.ca (Joseph B. Steinberg)URL: http://www.economics.utoronto.ca/steinberg/ (Joseph B. Steinberg)

Preprint submitted to Review of Economic Dynamics December 15, 2017

1c, and 1d show that, at the same time, the structure of global production has changed in threekey ways. First, emerging economies and the rest of the world have grown relative to advancedeconomies. Second international trade has grown substantially.1 Third, trade in intermediateinputs has grown faster than trade in final goods as documented by Hummels et al. (2001), Johnson(2014b), and Johnson (2014a), among others.

In the theoretical section of the paper, I derive a closed-form expression for equilibrium port-folios in a workhorse international macro model (Backus et al., 1994, 1995) with trade in in-termediate inputs and an arbitrary number of symmetric countries. In this setting, equilibriuminternational portfolio diversification is decreasing in country size, which is inversely related tothe number of countries, and increasing in trade in both final goods and intermediate inputs. Theseresults integrate and generalize the findings of Baxter and Jermann (1997), who argue that largercountries should hold more wealth in domestic assets, and Heathcote and Perri (2013), henceforthHP, who show that openness to trade increases diversification. For advanced economies, whoseshare of world GDP has fallen while their openness to trade has grown, these two forces worktogether. For emerging economies and the rest of the world, however, who have grown in bothsize and trade openness, these forces work in opposition. Thus, changes in the global productionstructure explain why international portfolio diversification has risen in advanced economies butnot in emerging economies and the rest of the world.

I also derive two new theoretical results about the effects of the global production structureon international portfolio diversification. First, openness to trade in intermediate inputs has thesame impact on portfolio diversification as trade in final goods. This suggests that the increasingshare of intermediate inputs in international trade has not contributed to the patterns in figure1a. My quantitative results are consistent with this prediction. Second, trade and country sizehave complementary effects on portfolio diversification. This provides insight into the differencesbetween the quantitative results for the United States and the results for other advanced economies.

In the quantitative section of the paper, I use a calibrated version of the model to assess thecontributions of changes in the global production structure to changes in portfolio diversification.This version of the model features four asymmetric regions — the same four regions in figure 1— and CES technologies that I calibrate to match input-output data from the World Input OutputDatabase (Timmer et al., 2015). To quantify the overall impact of changes in the global produc-tion structure on international portfolio diversification, I calibrate and solve the model twice, firstusing the 1995 input-output table and then using the 2011 table. The differences between thesetwo input-output tables capture all aspects of change in the global production structure between1995 and 2011: changes in relative country size, increased trade openness, and increased trade inintermediate inputs. The difference in each region’s equilibrium portfolio diversification betweenthese two calibrations is the model’s assessment of the combined impact of these changes on thatregion’s portfolio diversification. For advanced economies, overall change in the global produc-tion structure had a large impact on portfolio diversification. For the United States, equilibrium

1I measure each region’s openness to trade as the sum of its imports and exports as a fraction of world GDP, ratherthan the region’s own GDP. This measure disentangles changes in region size from changes in openness; using thestandard measure, a region that grows in relative size but not openness would trade more and thus affect other regions’openness. My quantitative exercise is designed with exactly this sort of disentanglement in mind.

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diversification rises by 7.33 percentage points, about a fifth of the increase observed in the data.For other advanced economies, diversification rises by 18.66 percentage points, more than half ofthe observed increase. For emerging economies and the rest of the world, equilibrium portfoliodiversification changes little in response to overall change in the global production structure, justas seen in the data.

To isolate the impacts of changes in the three features of the global production structure high-lighted above — country size, trade openness, and intermediate trade — I calibrate the model tocounterfactual input-output tables that I have constructed to capture what the global productionstructure would have looked like in 2011 had only one of these features changed at a time. Dif-ferences in equilibrium portfolio diversification between the 1995 calibration and these counter-factuals are the model’s assessments of each of these features’ effects on portfolio diversification.In the first counterfactual I change only each region’s relative size. Consistent with Baxter andJermann (1997)’s logic, equilibrium portfolio diversification rises in the U.S. and other advancedeconomies, which shrank in relative size, and falls in emerging economies and the rest of theworld, which grew. In the second counterfactual I change only each region’s openness to trade. AsHeathcote and Perri (2013) would predict, portfolio diversification rises in all regions, with largereffects in regions whose openness grew more. In the third counterfactual I change only the frac-tion of each region’s trade that is devoted to intermediate inputs. Consistent with my theoreticalanalysis, this change has little impact on portfolio diversification.

This paper contributes to several strands of literature. First and foremost, it contributes to thelarge literature on international portfolio diversification. Coeurdacier and Rey (2013) survey thisliterature and document the asymmetry between advanced and emerging economies that motivatesmy study. The inability of standard, one-good models to generate the degree of home bias ob-served in the data (Baxter and Jermann, 1997; Lewis, 1999) was once considered one of the mostimportant puzzles in the field (Obstfeld and Rogoff, 2001). Since then, numerous studies haveposed explanations for home bias in country portfolios. HP show that home bias emerges as anequilibrium outcome in standard international macro models in which domestic and foreign goodsare imperfect substitutes (Backus et al., 1994, 1995). Other explanations for are sticky prices (En-gel and Matsumoto, 2009), the presence of a nontraded sector (Hnatkovska, 2010), asymmetricinformation (Mondria and Wu, 2010; Dziuda and Mondria, 2012), and poor institutions (Mukher-jee, 2015). These studies have focused on accounting for levels of portfolio home bias rather thanchanges as I do in this paper. HP, though, point out that ”observed growth in trade. . . can explainonly a small fraction of the increase in international diversification. . . Investigating the causes ofthe residual growth in diversification is an interesting direction for future research.” My researchhelps fill this gap.

This paper is also related to the literature on the macroeconomic impact of increased inter-mediate trade. There is an active empirical literature that measures different aspects of this phe-nomenon, like vertical specialization (Hummels et al., 2001) and the decomposition of gross ex-ports into domestic and foreign value added (Johnson and Noguera, 2016; Johnson, 2014a; Koop-man et al., 2014; Wang et al., 2013). The input-output tables to which I calibrate my model capturechange in all of these measures. Quantitative research on the implications of increased trade inintermediate inputs has focused on international transmission of aggregate shocks. Bems et al.(2010), Bems et al. (2011), Bems et al. (2013), and others have studied the role of production

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chains in the collapse of global trade that followed the financial crisis of 2008–2009. Other worklike Arkolakis and Ramanarayanan (2009) and Johnson (2014b) study the role of production chainsin synchronizing business cycles across countries. These studies typically find that intermediatetrade has little impact on international business cycles. Similarly, I find that this phenomenon haslittle impact on portfolios.

Finally, my paper also makes a technical contribution to the literature on solving models withportfolio allocation problems. Perturbation methods that involve first-order approximations ofequilibrium conditions are not suitable for solving portfolio problems; these methods cannot de-termine equilibrium portfolios because all assets have the same expected return. Tille and vanWincoop (2010) and Devereux and Sutherland (2011) devise similar solution methods for two-country models that use higher-order approximations of the equilibrium conditions that governportfolio allocation. To solve for equilibrium portfolios in my model, which has four regions andan equal number of assets, I generalize the Devereux and Sutherland (2011) method to an environ-ment with any number of agents and assets. Models of portfolio choice with many agents and/orassets are often computationally intractable when using global solution methods, so my general-ized method should facilitate the investigation of a variety of interesting portfolio problems.

2. Theory

In this section I use a theoretical model to illustrate how the structure of global productionaffects equilibrium portfolio diversification. The model extends the workhorse international macromodel studied by HP to an environment with many symmetric countries that trade intermediateinputs, final goods, and equities. The number of countries, denoted by I, governs the size of eachcountry; as I increases each country i’s size relative to the size of the world economy falls.

In each period t = 0, 1, . . . the economy experiences an exogenous event st ∈ S ; the proba-bility of a history st = (s0, . . . , st) ∈ S t is π(st). Production firms in each country i produce grossoutput according to an input-output technology, combining domestic capital and labor with inter-mediate inputs produced both at home and abroad. Firms’ total factor productivities are subjectto country-specific productivity shocks that depend on the aggregate state st. Retailers in eachcountry combine domestic and foreign goods to produce a nontradable final good which is usedfor consumption and investment. Households in each country work, consume, and trade shares indomestic and foreign production firms.

2.1. Production firmsFirms in each country i use capital, ki(st), labor, `i(st), and intermediate inputs from each

country j, mi, j(st), to produce gross output according to the Cobb-Douglas technology

yi(st) =[zi(st)ki(st−1)α`i(st)1−α

]υ mi,i(st)µ∏

j,i

mi, j(st)1−µI−1

1−υ

. (1)

zi(st) is country i’s total factor productivity. In this section I assume that the stochastic processfor productivity is symmetric across countries but impose no other restriction. The parameter υ

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is the value added share in gross output. µ, the share of domestic inputs in the aggregate inter-mediate bundle, governs openness to intermediate input trade. Production firms choose factors,intermediate inputs, and investment, xi(st), to maximize the present value of dividends,

∞∑t=0

∑st∈S t

Qi(st)di(st), (2)

subject to a sequence of budget constraints,

di(st) = pi,i(st)yi(st) − wi(st)ni(st) −I∑

j=1

pi, j(st)mi, j(st) − xi(st), (3)

the usual law of motion for capital,

ki(st) = (1 − δ)ki(st−1) + xi(st), (4)

and the technology (1). pi, j(st) is the price of country j’s output relative to country i’s final goodand wi(st) is country i’s wage. Qi(st) is the price used to discount country i’s dividends.

2.2. RetailersCountry i’s final good, gi(st), is an Armington aggregate of purchases from each country j,

gi, j(st):

gi(st) = gi,i(st)ω∏

j,i

gi, j(st)1−ω1−I

. (5)

The parameter ω, the share of domestic inputs in the final demand bundle, governs openness totrade in final goods. Final demand aggregators are perfectly competitive, and choose inputs ineach period to maximize profits

gi(st) −I∑

j=1

pi, j(st)gi, j(st) (6)

subject to (5). The price of each country’s final good is normalized to one as in HP.

2.3. HouseholdsHouseholds in each country i have preferences

∞∑t=0

∑st∈S t

π(st)βtu(ci(st), `i(st)) (7)

over sequences of consumption, ci(st), and labor supply, `i(st). Households choose consumption,labor supply, and shares in each country j’s stock, λi, j(st), to maximize (7) subject to a sequenceof budget constraints,

ci(st) +

I∑j=1

ei, j(st)q j(st)(λi, j(st) − λi, j(st−1)

)= wi(st)`i(st) +

I∑j=1

λi, j(st−1)ei, j(st)d j(st). (8)

5

q j(st) is the price of country j’s stock and ei, j(st) is the real exchange rate between country i andcountry j. As in HP, I assume that flow utility is given by

u(ci(st), `i(st)) = log(ci(st)) − h(`i(st)) (9)

where h is increasing and convex. This allows for analytical characterization of equilibrium port-folios which do not depend on disutility from labor supply. Also as in HP, I assume that firms usedomestic households’ stochastic discount factors to price dividends: Qi(st) = π(st)βtci(s0)/ci(st).

2.4. EquilibriumA competitive equilibrium is a sequence of prices and quantities that satisfy: (i) the first-order

conditions of production firms, retailers, and households; (ii) market clearing conditions for grossoutput, final goods, and shares; and (iii) the law of one price. The market clearing conditions are,for each i = 1, . . . , I,

yi(st) =

I∑j=1

(m j,i(st) + g j,i(st)

), (10)

gi(st) = ci(st) + xi(st), (11)

1 =

I∑j=1

λ j,i(st). (12)

The law of one price requires that, for each i, j,

ei, j(st)p j, j(st) = pi, j(st). (13)

Equilibrium prices and allocations depend on initial conditions for each country’s productivity,capital stock, and portfolio holdings. For the remainder of section 2, I assume that initial conditionsfor capital stocks and portfolio shares are symmetric and all countries’ productivities start at theirunconditional mean values.

2.5. Characterizing equilibrium portfoliosThis environment, like that studied by HP and Heathcote and Perri (2004), admits an analyti-

cal solution for the equilibrium level of international portfolio diversification. Proposition 1 belowcontains this solution and Corollary 1.1 illustrates how it depends on the parameters that governthe structure of global production in the model, I, ω, and µ.

Proposition 1. There exists an efficient equilibrium in which each country holds a constant share λof domestic stock and a constant share (1−λ)/(I −1) of each foreign stock. International portfoliodiversification in this equilibrium is given by

1 − λ =(I − 1)(1 − Dω − F(1 − ω))

I − 1 + α [D + (I − 1)F − I(Dω + F(1 − ω))], (14)

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where the constants D and F are defined as

D =1 − µ − µυ − (I − 2)υ

Iµ + υ − Iµυ − I, (15)

F =(1 − υ)(µ − 1)

Iµ + υ − Iµυ − I. (16)

Proof. See the online appendix.

Corollary 1.1. If there is home bias in final demand (ω > 1/I) and in intermediate usage (µ > 1/I),equilibrium international portfolio diversification has the following properties:

(a) ∂(1−λ)∂I > 0, (b) ∂(1−λ)

∂ω> 0, (c) ∂(1−λ)

∂µ> 0,

(d) ∂2(1−λ)∂ω∂I > 0, (e) ∂2(1−λ)

∂µ∂I > 0.

2.6. DiscussionThe results above integrate and generalize those of Baxter and Jermann (1997) and HP. Baxter

and Jermann (1997) study a many-country, one-sector model in which domestic and foreign prod-ucts are perfect substitutes. Larger countries should have less internationally diversified portfolios,they argue, because such countries account for larger shares of world stock market capitalization.Property (a) of Corollary 1.1 captures this argument. HP study a two-country model in whichdomestic and foreign products are imperfect substitutes and find that portfolio diversification isincreasing in international trade in final goods. Property (b) captures this finding exactly. Theirsolution for equilibrium portfolios is, in fact, a special case of equation (14) with two countries(I = 2) and no intermediate inputs (υ = 1).

Properties (c)–(e) are novel results. Property (c) implies that trade in intermediates inputshas the same impact on portfolio diversification as trade in final goods. This is consistent withmy quantitative finding that the shift towards intermediate trade has had little impact on countryportfolios. Properties (d)–(e) imply that country size and trade openness have complementaryeffects on portfolio diversification. As we will see, these properties provide useful insight into thedifferences between the quantitative results for the United States, whose size and trade opennesshave changed modestly, and the results for other advanced economies, whose size and opennesshave changed significantly.

Putting these properties together, we can see how changes in the global production structureexplain the increase in portfolio diversification in advanced economies and the lack thereof inemerging economies and the rest of the world. For advanced economies, whose shares of worldoutput have shrunk while their openness to trade has grown, properties (a)–(c) of Corollary 1.1unambiguously predict rising diversification, just as we see in the data. For emerging economiesand the rest of the world, however, who have grown in both size and openness, property (a) has theopposite impact of properties (b) and (c). Consequently, the model does not make an unambiguousprediction about the change in portfolio diversification in emerging economies and the rest of theworld; quantitative analysis is necessary to investigate the contributions of each of these forces. Itake up that task in section 3.

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2.7. Risk sharing intuitionBefore turning to the quantitative analysis, however, I will first use risk-sharing theory to de-

rive some intuition for Proposition 1 and Corollary 1.1. Following HP, let ∆ci, j(st) denote theexchange-rate adjusted difference between consumption in country i and consumption in countryj: ∆ci, j(st) = ci(st) − ei, j(st)c j(st). Similarly, let ∆yi, j(st) and ∆xi, j(st) denote differences in nom-inal gross output and investment. Subtracting country j’s budget constraint from country i’s andassuming constant, symmetric portfolios, we find that

∆ci, j(st) = υ

1 − α

[1 −

(1 − IλI − 1

)]∆yi, j(st) +

(1 − IλI − 1

)∆xi, j(st). (17)

When I = 2 and υ = 1, this equation reduces to HP’s equation (18). Since the equilibrium exhibitsperfect risk sharing, ∆ci, j(st) = 0 for all i, j and all st.

In a one-good Lucas-tree model like that studied by Baxter and Jermann (1997), ei, j(st) alwaysequals 1 and ∆xi, j(st) always equals zero. In this case, perfect risk sharing implies that the solutionfor λmust set the coefficient on ∆yi, j(st) = 0. The solution is the same portfolio described in Baxterand Jermann (1997): 1 − λ = (I − 1)/(Iα).2 It entails a short position in domestic stock becauselabor and capital income are perfectly correlated. As the number of countries grows, internationalportfolio diversification rises; smaller countries have larger short positions in domestic stock. Thisaccounts for property (a) in Corollary 1.1.

In the model studied in this paper with Cobb-Douglas technologies and roundabout production,one can show that

∆ci, j(st) ∝ − ∆xi, j(st) +

(1 − IλI − 1

)∆xi, j(st)+

υ

1 − α

[1 −

(Iλ − 1I − 1

)] [I(Dω + F(1 − ω)) − 1

I − 1

]∆xi, j(st)). (18)

When portfolios are given by the solution in Proposition 1 the right hand side of this expressionis always equal to zero, confirming that this solution delivers perfect risk sharing. The last term,which HP call “indirect foreign financing,” is the source of the relationship between openness totrade and portfolio diversification. To see this, consider first the case without intermediate inputswhere υ = 1, D = 1, and F = 0. If there is home bias in final demand (ω > 1/I), an increase inrelative investment, ∆xi, j(st), raises relative demand for country i’s output. This improves countryi’s terms of trade, increasing the revenues of country i’s firms. The fraction of these additionalrevenues that accrue to domestic households is equal to the labor share plus domestic households’net claims to domestic capital income. This fraction is positive for standard values of α, yieldingcountry portfolios with long, not short, positions in domestic stock. When openness to trade infinal goods rises — when ω falls — the indirect effect becomes less important, however, andportfolio home bias falls. This accounts for property (b).

2In the online supplement I show that in this simple model environment my numerical method replicates thissolution exactly for any number of countries.

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In the model with intermediate inputs, the size of the indirect financing effect is determined bythe composite trade openness parameter Ω ≡ Dω+ F(1−ω). The constants D and F represent theamounts of domestic and imported gross output, respectively, needed to accommodate a one-unitincrease in domestic absorption. With home bias in both final demand and intermediate usage,the indirect financing effect is positive because IΩ is greater than one; an increase in relativeinvestment still boosts relative demand for domestic gross output and thus the terms of trade.Moreover, Ω is increasing in both ω and µ, so openness to trade in final goods and opennessto trade in intermediate inputs have the same effect on indirect financing.3 Consequently, bothtypes of trade have the same effect on international portfolio diversification. This accounts forproperty (c) and explains why increasing the intermediate trade share has little impact on portfoliodiversification in the quantitative analysis.

The indirect financing effect also accounts for properties (d) and (e), the complemtarities be-tween country size and trade openness. When I is large — and each country is relatively small —changes in the trade openness parameters, ω and µ, have a larger impact on the term (IΩ−1)/(I−1)which governs the size of the indirect effect.

3. Quantitative strategy

To measure the effects of changes in the global production structure on international port-folio diversification, I use a quantitative version of the model to construct a mapping betweeninput-output data and equilibrium portfolios. To assess the overall impact of change in the globalproduction structure, I calibrate the model to input-output tables for 1995 and 2011, and then com-pare equilibrium portfolio diversification in the two calibrations. To assess the effects of changesin different aspects of the global production structure — country size, trade openness, and inter-mediate input trade — I construct counterfactual input-output tables for 2011 in which only oneof these aspects changes.

To make the changes in model portfolios comparable with the data, I calibrate wedges inhouseholds’ portfolio-choice first-order conditions so that the model matches each region’s 1995level of portfolio diversification. Thus, when calibrated to 1995 input-output data, the modelreplicates both the global production structure and portfolio diversification for that year. I holdthese wedges fixed when using real or counterfactual data for 2011, which allows me to analyzehow changes in the global production structure affect international portfolio diversification holdingconstant other factors that might affect country portfolios. Mukherjee (2015) shows that thesewedges can result from cross-country differences in institutions and corporate governance, forexample; the residual portfolio diversification growth that the model does not capture could be theresult of financial development.

3.1. Quantitative modelThe quantitative model has I = 4 asymmetric “countries” that correspond to the regions in

figure 1 and a more general input-output structure for production and demand.

3Ω is increasing in ω because D > F. It is increasing in µ because D (F) is increasing (decreasing) in µ.

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Gross output production technologies in this version of the model have a nested CES structure:

yi(st) =

υ1η

i

[zi(st)ki(st−1)α`i(st)1−α

] η−1η

+ (1 − υi)1η

I∑j=1

µ1ζ

i, jmi, j(st)ζ−1ζ

(η−1)ζη(ζ−1)

ηη−1

. (19)

υi, the share of value added in gross output, and µi, j, the share of intermediates sourced fromcountry j, vary across countries. η and ζ, the elasticities of subsitution between value added andintermediates and between intermediates from different sources, respectively, are the same acrosscountries.

Consumption and investment are Armington aggregates of domestic and foreign products:

ci(st) =

I∑j=1

ω1ρ

i,c, jci, j(st)ρ−1ρ

ρρ−1

(20)

xi(st) =

I∑j=1

ω1ρ

i,x, jxi, j(st)ρ−1ρ

ρρ−1

, (21)

Again, the expenditure share parameters, ωi,c, j and ωi,x, j differ across countries, while the elasticityof substitition between domestic and foreign final goods, ρ, is not country-specific.

Finally, household preferences take the parametric form:

ui(ci(st), `i(st)) =ci(st)1−γ

1 − γ−

(θi

1 + ψ

) (`i(st)Θi

)1+ψ

. (22)

The parameters θi and Θi, which govern disutility from labor supply and labor endowments, differacross countries, while risk aversion and the Frisch elasticity, γ and ψ, do not. Following Tilleand van Wincoop (2010), financial frictions distort households’ returns from investing in foreignstocks. I model these frictions as wedges in households’ portfolio-choice first-order conditions.The first-order condition for country i’s choice of country j’s stock is

u′(ci(st))pi,c(st)

=∑

st+1∈S

π(st, st+1)βu′(ci(st, st+1))pc,i(st, st+1)

R j(st, st+1)eτi1i, j , (23)

where

R j(st, st+1) =q j(st, st+1) + d j(st, st+1)

q j(st), (24)

and τi is country i’s wedge on foreign stock returns.4 When the model is calibrated to 1995input-output data, I choose these wedges to match each region’s level of international portfoliodiversification in that year. When the model is calibrated to real or counterfactual input-outputdata for 2011, I do not recalibrate the wedges. This allows for direct comparison of changes inportfolio diversification over time between the model and the data.

4In section 2 I normalized the price of each country’s consumption good to one as in HP. This approach makesapplying the Devereux and Sutherland (2011) method cumbersome, however, so in the quantitative model I choosea single numeraire good (the rest of the world’s consumption good) instead; pi,c(st) denotes the price of country i’sconsumption relative to the numeraire.

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3.2. Solving for equilibrium portfoliosTo solve for steady-state portfolios in the quantitative model I use the method of Devereux

and Sutherland (2011), which involves a combination of first- and second-order approximationsto the equilibrium conditions. Below, I briefly describe how to generalize their method to a many-country, many-asset environment like the one that I study in this paper. More details and exampleprograms can be found in the online appendix.

We can combine the first-order conditions for country i’s choices of stocks j and I as

0 =∑

st+1∈S

π(st, st+1)u′(ci(st, st+1))pi,c(st, st+1)

(R j(st, st+1)eτi1i, j − RI(st, st+1)eτi1i,I)

), ∀ j < I. (25)

The non-stochastic steady-state version of equation (25), which implies that all stocks have thesame return, is dependent across countries, so non-stochastic steady-state portfolios are indeter-minate. A first-order approximation, which implies that all stocks have the same expected return,is also dependent, so portfolios are still indeterminate.5 A second-order approximation, though,yields an independent set of equations given by

0 =∑

st+1∈S

π(st, st+1)[R j(st, st+1) − RI(st, st+1) +

12

(R j(st, st+1)2 − RI(st, st+1)2

)+

(−γci(st, st+1) − pi,c(st, st+1)

) (R j(st, st+1) − RI(st, st+1)

)+ eτi1i, j − eτi1i,I

], ∀ j < I,

(26)

where hats denote log-deviations from a variable’s steady-state value. Combining (26) for coun-tries i and I, we get

0 =∑

st+1∈S

π(st, st+1)[ (−γci(st, st+1) − pi,c(st, st+1) + γcI(st, st+1) + pc,I(st, st+1)

)×

(R j(st, st+1) − RI(st, st+1)

)+ eτi1i, j − eτi1i,I − eτI + 1

], ∀ j < I. (27)

Steady-state portfolios must satisfy equation (27) for all i < I and all j < I. This equation consistssolely of product terms (except for the wedges which are parameters), so first-order approxima-tions are sufficient to evaluate this equation to second-order accuracy. Thus, given a candidatesolution for steady-state portfolios, we can linearize the non-portfolio variables and equilibriumconditions and check whether equation (27) is satisfied. When I = 2, as in Devereux and Suther-land (2011), there is a single equation that must be solved. When I > 2, as in this paper, steady-state portfolios solve the system formed by stacking the equation blocks (27) for each countryi < I. This generalization works for any portfolio choice problem, regardless of the number ofagents and assets.

5As in Tille and van Wincoop (2010), the wedges, τi, are assumed to be second-order so they do not enter zero-and first-order approximations of the equilibrium conditions. Moreover, in a second-order approximation productterms involving the wedges drop out.

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3.3. Calibration procedureMy calibration procedure has three steps. First, I assign some parameters like elasticities of

substitution to common values in the literature and estimate a joint process for the productivityshocks zi(st). Table 2 lists this first group of parameters, which I hold fixed in all calibrations.Second, I set the remaining parameters so that the model’s non-stochastic steady state replicatesone of several input-output tables that I describe below. Table 6 lists the parameters in this sec-ond group for each of the input-output tables I use in my quantitative analysis. Third, if using1995 input-output data to calibrate the production parameters I also calibrate the portfolio-choicewedges, τi, so that each region’s international portfolio diversification in the model matches the1995 data. The calibrated values of these wedges can also be found in table 2.

3.3.1. Assigned parametersThere are three elasticities of substitution that must be assigned. I set the elasticity of substi-

tution between value added and intermediates, η, to Atalay (2017)’s estimate of 0.05. Kehoe et al.(Forthcoming) show that this value is consistent with the dynamics of the U.S. gross output/GDPratio. I set the final and intermediate Armington elasticities, ρ and ζ, to one, a standard value inthe international macro literature. In my sensitivity analysis, I show that my results are robustto these choices. Other assigned parameters govern capital formation and preferences. I set thedepreciation rate, δ, and the capital share, α, to standard values of 0.06 and 0.36, respectively. Iset the discount factor, β, to 0.96 so that the steady-state real interest rate is 4% per year. As in HP,I set risk aversion and the Frisch elasticity each to one: γ = ψ = 1.

3.3.2. Productivity processI estimate a stochastic process for productivity of the form

log z1(st)log z2(st)log z3(st)log z4(st)

= P

log z1(st−1)log z2(st−1)log z3(st−1)log z4(st−1)

+

ε1(st)ε2(st)ε3(st)ε4(st)

, (28)

where the matrix P governs persistence and spillovers. The innovations, εi(st), are drawn froma joint normal distribution with variance-covariance matrix Σ. I use the Penn World Tables tocalculate region-level TFP series. The goal of the PWT is to construct data on output and othermacroeconomic variables that are measured in consistent units across countries, so this data iswell-suited to aggregating output and factors of production within each region. The online ap-pendix describes the treatment of the PWT data in more detail. I find that TFP in the EME andROW regions is somewhat less persistent and substantially more volatile than TFP in the UnitedStates and the ADV region. This is consistent with the findings of other studies that estimate TFPprocesses for a wide range of countries (see, e.g., Bai and Zhang, 2010). I also find substantialspillovers from the United States to the ADV and ROW regions.

3.3.3. Parameters calibrated to input-output dataGiven the values of the fixed parameters, I calibrate the remaining parameters (except for the

portfolio wedges, τi) so that the model’s nonstochastic steady state matches one of the benchmark12

or counterfactual input-output tables described below. My approach is simple: I plug the input-output table data into the model’s equilibrium conditions and back out the implied parametervalues. Panel (a) of table 3 shows how one can represent all of the model’s steady-state quantitiesin an input-output table. Rows indicate source and columns indicate destination. The last rowand column contain gross output and the penultimate row contains value added. Without loss ofgenerality I assume all steady-state prices are one.

First, I calibrate the intermediate expenditure shares, µi, j. For example, combine country i’sfirst-order conditions for inputs from countries j and k to obtain:

p j

pk= 1 =

(µi, j

µi,k

mi,k

mi, j

). (29)

Normalizing∑N

j=1 µi, j = 1, we can immediately recover all values of µi, j. I use a similar procedureto recover the expenditure shares for consumption, ωi,c, j, and investment, ωi,x, j, and the shares ofvalue added in gross output, υi. The weights on disutility from labor, θi, can be recovered by usingsteady-state consumption and labor supply in households’ intratemporal optimality conditions.Each country’s labor endowment, Θi, is set to a fraction 1 − α of its value added.

3.3.4. Portfolio wedgesWhen using the 1995 input-output data to calibrate the production parameters, I also calibrate

the portfolio wedges, τi, so that each region’s equilibrium international portfolio diversification inthe model is the same as in the 1995 data. I assume that each country’s wedge is proportional tothe autocovariance of its TFP innovation. This ensures that the the wedges are second-order termsthat do not affect the equilibrium dynamics of non-portfolio variables and ensures that portfoliosare well-behaved (Tille and van Wincoop, 2010). When using 2011 input-output data (real orcounterfactual), I do not recalibrate the wedges.

3.4. Input-output dataThe input-output tables used in my quantitative analysis are based on data from the World

Input Output Database (Timmer et al., 2015), henceforth WIOD, which publishes world input-output tables for each year between 1995 and 2011. Each WIOD input-output table reports grossoutput, value added, intermediate inputs, and final demand for 40 countries and 35 industries. Iaggregate all industries into a single production sector and aggregate countries into four regions:the United States (USA); other advanced economies (ADV); emerging economies (EME); andthe rest of the world. Table 1 lists the countries in each region.6 The online appendix containsadditional details about the treatment of the input-output data.

6The rest of the world represents developing countries that do not yet have quality national input-output data. TheWIOD constructs the rest of the world’s gross output and final demand by reconciling the national accounts of the40 countries in the database with total world output and final demand in the UN National Accounts. The rest of theworld’s intermediate input matrix is constructed by averaging the data for key emerging economies in the database:Brazil, China, India, Indonesia, Mexico, and Russia. Consequently, the rest of the world is similar to the EME regionby construction; one can loosely think of it as a second emerging-economy region.

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To measure the overall impact of change in the global production structure I calibrate the modelto input-output tables for 1995 and 2011, the first and last years available in the WIOD. Trade isunbalanced in the raw WIOD data, however, which poses a challenge for interpreting these dataas steady states in the model. In a steady state, the balance of payments implies that a country’snet foreign assets are equal to the product of the interest rate and that country’s trade deficit.The United States, for example, which runs trade deficits, would have a positive (and very large)net foreign assets position, while emerging economies, which run trade surpluses, would havenegative net foreign assets. This is sharply at odds with the data. To solve this problem, I use theRAS procedure (Bacharach, 1965) to construct similar input-output tables in which each region’ssize, trade openness, and intermediate trade share are the same as in the raw data but each region’saggregate trade is balanced. This procedure is commonly used in input-output analysis to reconcileinput-output tables with data on national income accounts and industry output. The U.S. Bureauof Economic Analysis and other national statistical agencies, for example, use RAS to updatenational input-output tables between benchmark years, and Johnson and Noguera (2016) use asimilar method to reconcile input-output tables, national accounts, and trade data from differentsources. The online appendix contains a detailed description of the procedure.

Panels (b) and (c) of table 3 show the balanced input-output tables for 1995 and 2011, respec-tively.7 In what follows, I refer to them as the 1995 and 2011 benchmarks. Panels (a) and (b) oftable 5 list each region’s size, trade openness, and intermediate trade share in the two benchmarks,and the first two columns of table 6 list the parameter values that have been calibrated using thebenchmark data.

To separate the effects of changes in region size, trade openness, and intermediate trade, I con-struct counterfactual input-output tables that represent what the global production structure wouldhave looked like in 2011 had only one of these dimensions changed at a time. In each counterfac-tual, I use the RAS procedure to construct an input-output table that matches the 2011 benchmarkdata for one of these dimensions but is otherwise similar to the 1995 benchmark. One might ask:why not simply change the parameters that govern, for example, region size while leaving all otherparameters fixed at their 1995 values? The drawback of this alternative approach is that other as-pects of the global production structure would change endogenously in equilibrium as well. Ifone were to change labor endowments, which govern region size, but hold all other parametersfixed, trade openness and intermediate trade shares would change endogenously in response. Thisalternative exercise would not separate the effects of region size on country portfolios from theeffects of other aspects of the global production structure. Using the RAS procedure to constructcounterfactual input-output data eliminates these general equilibrium effects, allowing me to iso-late the effects of region size, trade openness, and intermediate trade one at a time. Table 4 showsthe input-output tables that I have constructed for each counterfactual.

3.4.1. Counterfactual 1: changes in country size onlyIn the first counterfactual, I construct an input-output table that is similar to the 1995 bench-

mark except that each region’s size changes to match the 2011 data. Panel (c) of table 5 shows that

7I have lumped consumption and investment into a single “final demand” category to make the tables easier toread. The full tables can be found in the appendix.

14

while the counterfactual has the same distribution of world GDP as the 2011 benchmark (and thisis by construction), in other respects the counterfactual is indeed similar to the 1995 benchmark:trade openness and intermediate trade shares are close to their 1995 values. Column 3 of table 6lists the calibrated parameters in this counterfactual. The labor endowments, Θi, are the same asin the 2011 benchmark because these parameters map directly to each region’s size. The labordisutility parameters, θi, change as well because each region’s consumption grows in proportionto its GDP. The other parameters are similar to their 1995 benchmark values. There are smallchanges in the Armington share parameters that reflect the general equilibrium effects of changesin labor endowments. If expenditure shares did not change, advanced economies, which shrank,would trade less while emerging economies and the rest of the world, which grew, would trademore.

3.4.2. Counterfactual 2: changes in trade openness onlyThe second counterfactual is similar to the 1995 benchmark except that each region’s trade as

a share of world GDP changes to match the 2011 data. Panel (d) of table 5 verifies that whiletrade openess rises, region size and intermediate trade shares in this counterfactual are similarto the 1995 benchmark data. Column 4 of table 6 lists the calibrated parameters for the secondcounterfactual. This time, labor endowments and disutilities remain at their 1995 benchmarklevels while the expenditure share parameters change. They do not change exactly as in the 2011benchmark, though; if they did, the counterfactual would not be consistent with the 2011 tradeopenness data because region size does not change.

3.4.3. Counterfactual 3: changes in intermediate inputs onlyIn the last counterfactual, each region’s size and total trade openness stay fixed at 1995 bench-

mark levels but each region’s intermediate trade share rises to match the 2011 data. The lastcolumn of table 6 shows that, as in the second counteractual, labor endowments and disutilityparameters stay fixed at 1995 benchmark values while the expenditure share parameters change.This time, the domestic intermediate Armington shares, µi,i, fall while the imported intermediateshares rise; the reverse happens for consumption and investment Armington shares. Once again,note that the changes in these share parameters incorporate general equilibrium effects of increasedintermediate trade and reduced final goods trade.

4. Quantitative results

Having described the quantitative version of the model, the solution method, the calibrationprocess, and the treatment of the input-output data, I now present the results of the analysis. Panel(a) in table 7 lists the observed change in each region’s international portfolio diversification be-tween 1995 and 2011 alongside the model predictions in the benchmark and counterfactual exer-cises.

4.1. Data: observed changes in international portfolio diversificationI measure each region’s international portfolio diversification as the GDP-weighted average of

the international portfolio diversification levels of the countries that comprise that region. I use

15

the same measure of country-level international portfolio diversification as HP: foreign assets andliabilities as a percent of total country wealth. The online supplement provides further details onthese calculations. Figure 1a and the first column of table 7 show how each region’s portfolio di-versification evolved between 1995 and 2011. As I have discussed above, the asymmetry betweenadvanced and emerging economies is stark: diversification in the United States and other advancedeconomies rose dramatically, while diversification in the EME and ROW regions rose little or notat all.

There is one complication that arises in comparing the results of the quantitative analysis tothese data. The Lane and Milesi-Feretti dataset that I use to compute country-level internationalportfolio diversification reports multilateral foreign asset and liability positions only—not bilateralpositions. Consequently, I cannot distinguish between inter- and intra-regional asset holdings. Forexample, German foreign assets, which count towards the ADV region’s portfolio diversification,likely include assets issued by France, another country in the ADV region, as well as assets issuedby non-ADV countries. Thus, my measure of regional international portfolio diversification maybe biased upward. It is not possible to ascertain whether this bias has waxed or waned over time.The U.S. data are unbiased, however, and show that the increase in advanced economies’ portfoliodiversification is not purely an artifact of the data. Moreover, the changes in regional diversificationare unbiased as long as the bias in diversification levels has not changed over time, and thesechanges are the focus of this paper. The model’s predicted changes in regional diversification arenot sensitive to the initial levels to which the model is calibrated; in an earlier version of the paperwhich did not include the wedges used to match initial diversification levels, I obtained similarresults for each region’s change in diversification.

4.2. Benchmark: overall change in the global production structureThe first stage of the quantitative analysis asks: how did overall change in the global produc-

tion structure affect international portfolio diversification? To answer this question, I compare thechange in each region’s portfolio diversification between the 1995 and 2011 benchmark calibra-tions with that region’s change in diversification in the data. The change in portflio diversificationbetween the two benchmark calibrations is shown in the second column of panel (a) in table 7.

The results of the benchmark exercise indicate that for advanced economies, changes in theglobal production structure account for much of the increase in portfolio diversification observedin the data. For the United States, portfolio diversification rises by 7.33 percentage points in thebenchmark model, 19.96 percent of the observed increase. For other advanced economies, themodel generates an increase of 18.66 percentage points, or 50.67 percent of the observed increase.The model’s predictions are also consistent with the small increases in diversification observed inemerging economies and the rest of the world. Both results support the theory advanced in section2.

The benchmark results also indicate, though, that other factors are also important in explainingpatterns of portfolio diversification growth across regions. In advanced economies, particularlythe United States, the observed increase in diversification is larger than in the benchmark model.Technological innovations that reduced information asymmetries may be important in explainingresidual growth in advanced economies’ portfolio diversification (Mondria and Wu, 2010; Dziudaand Mondria, 2012). For the other two regions, particularly the rest of the world, financial frictions

16

and other institutional problems may have contributed to the persistence of home bias (Mukher-jee, 2015). In section 5.4 I show that rising trade imbalances may also have contributed to theasymmetry in portfolio diversification growth between advanced and emerging economies.

4.3. Counterfactual 1: changes in size onlyThe first counterfactual exercise asks: how did changes in region size affect international port-

folio diversification? In this exercise, counterfactual model predictions are given by the differencebetween each region’s portfolio diversification in the 1995 benchmark and that region’s diversifi-cation in the first counterfactual calibration for 2011. The third column of panel (a) in table 7 liststhese predictions.

The results of the first counterfactual indicate that changes in the distribution of world outputcontributed significantly to the asymmetry in portfolio diversification growth between advancedand emerging economies. For the United States and other advanced economies, which shrank inrelative size, portfolio diversification rises in the counterfactual. The increase is larger for the ADVregion whose share of world GDP fell more. In emerging economies and the rest of the world,whose relative sizes grew, portfolio diversification falls in the counterfactual. In short, holdingother aspects of the global production structure fixed, changes in region size are inversely relatedto changes in portfolio diversification.

4.4. Counterfactual 2: changes in trade openness onlyThe second counterfactual asks: how did changes in openness to international trade affect

portfolio diversification? Counterfactual model predictions in this exercise are constructed in asimilar manner as in the first counterfactual. They are listed in the fourth column of panel (a) intable 7.

The results of the second counterfactual show that increased trade openness raised portfoliodiversification in all regions. Moreover, regions with larger increases in openness have largercounterfactual increases in diversification. The EME and ROW, whose openness rose most, havethe largest counterfactual increases in diversification, while the United States, where opennessrose least, has the smallest increase in diversification. As a result, increased openness reduced theasymmetry in portfolio diversification growth between advanced and emerging economies.

The theoretical analysis in section 2 supports these results and provides some additional con-text. Properties (d) and (e) of Corollary 1.1, in particular, illustrate why increased trade opennesshas such a large impact on diversification in emerging economies and the rest of the world andsuch a small impact in the United States. The EME and ROW regions are small relative to theadvanced economies, which makes their portfolios sensitive to changes in trade openness. TheEME and ROW regions were also smaller in 1995 than they were in 2011; their growth in size inthe benchmark exercise mitigates the impact of their growth in openness. For the United States,which is large relative to other regions and shrank between 1995 and 2011, the reverse is true.

4.5. Counterfactual 3: changes in intermediate trade shares onlyThe third counterfactual asks: how did increased intermediate goods trade affect portfolio

diversification? The last column of panel (a) in table 7 lists the results for this exercise.

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All four regions have small changes in diversification in this counterfactual, which indicatesthat the shift towards intermediate goods trade has not significantly affected country portfolios.This is consistent with the theory advanced in section 2, which shows that trade in intermediategoods has a similar impact on portfolios as trade in final goods. In model simulations I have foundthat the covariance of domestic capital and labor income, which HP show is a key determinant ofhome bias in country portfolios, differs little between the 1995 benchmark and this counterfactual.These results are supported by recent findings in the international macroeconomics literature thatinternational input-output linkages do not significantly affect international business cycle proper-ties (Arkolakis and Ramanarayanan, 2009; Johnson, 2014b).

4.6. Changes in bilateral portfolio holdingsThus far, my analysis has focused on the impact of changes in the global production structure

on international portfolio diversification. One might also ask: how does the structure of globalproduction affect bilateral portfolio holdings? The United States and other advanced economies, inparticular, have become more internationally diversified. Towards which regions’ stocks have theUnited States and other advanced economies reallocated their portfolios? The Lane and Milesi-Ferretti (2007) data and the symmetric theoretical model presented in section 2 do not permitanalysis of bilateral portfolio holdings, but we can investigate the predictions of the quantitativemodel.

Panel (a) of table 9 lists the changes in each region’s bilateral portfolio shares in the benchmarkexercise. The results show that the decrease in home bias in the United States and other advancedeconomies comes primarily from a shift towards the EME region’s stock. This is due in part tothe fact that the EME region grew most rapidly; Baxter and Jermann (1997) and property (a) ofCorollary 1.1 suggest that faster-growing countries should receive more foreign equity investment.Advanced economies’ reallocation towards EME stock may also be due to the fact that advancedeconomies’ trade with the EME region grew more than their trade with each other and the rest ofthe world. The EME region, whose home bias did not change much, shifted its portfolio awayfrom USA stock towards ROW stock. Similarly, the ROW region shifted from USA stock towardsEME stock. This may be due in part to the fact that the EME and ROW regions’ trade with eachother grew rapidly while their trade with the United States grew slowly.

Panels (b)–(d) of table 9 list the changes in bilateral portfolio holdings in each of the threecounterfactual exercises. Changes in the global production structure account for these results aswell. In the first counterfactual, all regions reduce their holdings of shrinking regions’ stocksand increase their holdings of growing regions’ stocks. In the second counterfactual, changes inbilateral portfolio shares are consistent with changes in bilateral trade: each region reallocatestowards the stocks of other regions with which its trade grows most. In the last counterfactual,in which portfolio diversification does not change significantly, bilateral portfolio shares changelittle as well.

5. Sensitivity analyses

I have conducted a wide range of additional experiments with my quantitative model. My mainresults about the impact of the global production structure on international portfolio diversification

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are robust to changes in many of the model’s assigned parameters, functional forms, and otherassumptions. In this section, I present the results from several sensitivity analyses which provideadditional context for my findings. In each analysis below, I recalibrate all model parameters usingthe procedure described in section 3.3.

5.1. Armington elasticitiesThe Armington elasticity of subsitution between domestic and imported goods plays a cru-

cial role in determining home bias in country portfolios. In one-good models like that studied byBaxter and Jermann (1997), where domestic goods and imports are perfect substitutes, equilib-rium portfolios entail large short positions in domestic assets. By contrast, models with imperfectsubstitutability like that studied in section 2 of this paper yield the opposite result; HP show thatin such models the level of international portfolio diversification is sensitive to the Armingtonelasticity. Here, I ask: does the Armington elasticity affect the relationship between the globalproduction structure and equilibrium portfolios?

In my theoretical analysis and my baseline quantitative exercises I assumed a unitary Arm-ington elasticity; common values in international macroeconomics range from 0.9 to 2.0. Panel(b) of table 7 repeats the quantitative exercise using a higher Armington elasticity of 1.25 forboth intermediate and final goods. Overall, the global production structure has less impact onportfolio diversification in this version of the analysis. In the counterfactuals, size and opennessto trade have less impact while intermediate trade has slightly more impact. In panel (c), whichuses a lower elasticity of 0.75 for both final and intermediate goods, the results are reversed, andincreasing the intermediate share of trade actually lowers diversification (although this effect isonce again small). Quantatively, though, the results of both sensitivity analyses are similar to thebaseline results.

Little is known about whether Armington elasticities are higher for intermediate goods or forfinal goods. In order to analyze the sensitivity of my results to the relative Armington elasticity inintermediate trade, I raise or lower the intermediate Armington elasticity, ζ, and change the finalArmington elasticity, ρ, in the opposite direction in order to stabilize the aggregate elasticity usingthe approach suggested by Johnson (2014b). Panel (d) of table 7 lists the results with a higher elas-ticity for final goods, and panel (e) lists the results with a higher elasticity for intermediate goods.None of the results change much in these analyses. One thing stands out, though: the effect ofintermediate trade (counterfactual 3) is minimized when final goods and intermediate goods havethe same Armington elasticity. When final goods are more substitutable (panel (d)), increasing theintermediate trade share has a larger impact on portolios than in the baseline analysis. When in-termediate goods are more substitutable (panel (e)), increasing the intermediate trade share lowersdiversification, but the magnitude of the effect is again larger than in the baseline. This is con-sistent with the findings of Baqaee and Farhi (2017), who show that Cobb-Douglas technologiesminimize the role of intermediate linkages in propagating sectoral — or in this case, regional —shocks.

5.2. Risk aversionIn my theoretical analysis and baseline quantitative results, I assumed that households have log

utility. When households are more risk averse, the need to hedge real exchange rate risk creates19

an additional motive for diversification (Coeurdacier, 2009; van Wincoop and Warnock, 2010;Coeurdacier and Rey, 2013). HP show that risk aversion has a significant impact on the level ofhome bias in country portfolios in BKK models. Here, I ask: how does risk aversion affect therole of the global production structure in determining international portfolio diversification?

In panel (f) of table 7, I present the results from a version of the quantitative analysis when riskaversion, γ, is set to 2. In this version of the analysis, the overall impact of the global productionstructure on portfolio diversification is smaller than in the baseline analysis and the asymmetrybetween advanced and emerging economies disappears. This is because region size has a smallerimpact than in the baseline but trade openness still has a significant impact, and the latter is moreimportant for the EME and ROW regions. The difference in results in the first counterfactualsuggests that region size may affect the strength of the real exchange rate hedging motive. Thismay be an interesting avenue for future research.

5.3. Stochastic processIn the theoretical model studied in section 2 the stochastic process for regional productivity

does not affect equilibrium portfolios because the competitive equilibrium replicates the efficientallocation for any arbitrary symmetric process. The quantitative model has two features that couldmake markets incomplete. First, regions are asymmetric. Second, intermediate inputs and valueadded are imperfect substitutes — in fact, they are almost perfect complements. Both featuresprevent me from obtaining theoretical proof of financial market completeness and thus could affectequilibrium portfolios. Here, I ask: does the stochastic process for regional productivity matter forequilibrium portfolios in the quantitative model? If so, how does the stochastic process affect therole of the global production structure in determining international portfolio diversification?

Panel (b) of table 8 presents the results from a version of the analysis without productivityspillovers. In this version, I estimate independent stochastic processes for regional productivity ofthe standard AR(1) form

log zi(st) = ρi,z log zi(st−1) + εi(st), (30)

where εi are independently drawn from normal distributions with region-specific variances σ2i .

The parameters of the estimated independent productivity processes are

ρi,z =[0.69 0.87 0.67 0.65

], σ2

i =[0.00015 0.00018 0.00046 0.00046.

](31)

These values are similar to the diagonals of the P and Σ matrices that represent the joint produc-tivity process in the baseline model. The results in this version of the analysis are similar to thebaseline results, but changes in the global production structure have less impact on diversificationin both the benchmark and counterfactual exercises. Thus, the model’s stochastic structure doesindeed affect equilibrium portfolios. In particular, the correlation between regional productivitiesobserved in the data appears to amplify the effects of the global production structure on portfoliodiversification. This suggests that increased international business cycle synchronicity (see, forexample, Perri and Quadrini, 2011) may have contributed to the trends depicted in figure 1a.

To investigate why the stochastic structure affects equilibrium portfolios, I conduct two morerelated sensitivity analyses. In the first, shown in panel (c) of table 8, I set the elasticity of sub-stitution between value added and intermediate inputs, η, to one and use the correlated stochastic

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process from the baseline model. These results are similar to the baseline results, but differentenough to suggest that complementarity between value added and intermediates prevents marketcompleteness in this environment. In panel (d), I set η to one and use the independent productivityprocesses estimated above. These results are similar, but not equal to, the independent-productivityresults in panel (b). This indicates that regional asymmetries also prevent market completeness. Icannot prove these conclusions theoretically, though, so further research is needed on this front.

5.4. Trade imbalancesIn the baseline analysis I have assumed that each region’s steady-state trade balance is zero in

the two benchmark input-output tables and in the three counterfactuals. Between 1995 and 2011,however, regional trade balances diverged: advanced economies’ trade balances fell while tradebalances in emerging economies and the rest of the world rose. This trend represents a fourth wayin which the global production structure changed during this period. In this sensitivity analysis, Iask: what is the role of trade imbalances in determining international portfolio diversification?

Panel (a) of table 10 presents the results of a version of the quantitative analysis in which Ido not impose balanced trade. In this version of the analysis, I use the raw 1995 and 2011 input-output data without modification. The benchmark exercise in this version of the analysis capturesthe effects of diverging trade balances as well as changes in region size, trade openness, andintermediate trade. I also include a fourth counterfactual exercise in which I construct an input-output table that matches 2011 trade balances but is otherwise similar to the 1995 benchmark.This counterfactual isolates the effect of trade imbalances on portfolio diversification. In eachcalibration, I use the steady-state version of the balance of payments conditions to infer steady-state net foreign assets. Each region’s steady-state net foreign asset position is set equal to thenegative of its trade balance divided by the steady-state interest rate of 4 percent. Thus, regionswith trade deficits have positive net foreign asset positions, while regions with trade surpluses havenegative positions.

In the unbalanced-trade version of the benchmark exercise, portfolio diversification growsmore in advanced economies than in the baseline analysis, rises less in emerging economies, andfalls in the rest of the world. In other words, trade imbalances magnify the asymmetry in portfoliodiversification growth between advanced and emerging economies. The drop in the rest of theworld’s diversification is likely due to the fact that this region had a large trade deficit in 1995; thisdeficit shrank soon after the spate of sudden stop episodes in the late 1990s. In the unbalanced-trade versions of the first three counterfactuals, region size and intermediate trade have similareffects as in the baseline analysis, while trade openness has a larger effect except in the rest of theworld. In the new fourth counterfactual exercise, changes in trade balances are positively corre-lated with changes in diversification. Falling trade balances raised advanced economies’ portfoliodiversification, while rising trade balances lowered diversification in emerging economies and therest of the world. The effects of trade imbalances in the fourth counterfactual are of comparablesize to the effects of region size and trade openness in the first two counterfactuals.

Incorporating trade imbalances introduces an additional source of asymmetry across regions,so I redo the sensitivity analysis from section 5.3 to investigate whether trade imbalances affectthe role of the stochastic process in determining equilibrium portfolios. Panels (b)-(d) of table 10

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present the results of the unbalanced-trade versions of the analyses with independent productivi-ties, Cobb-Douglas technologies, and both modifications, respectively. The effect of trade imbal-ances (the fourth counterfactual) varies substantially across the four versions of the unbalanced-trade analysis, indicating that this additional source of asymmetry indeed amplifies the impact ofthe stochastic process on equilibrium portfolios.

The results of the unbalanced-trade analyses indicate that diverging trade balances have hada significant impact on international portfolio diversification. Caution should be taken when in-terpreting these results, however, because steady-state net foreign asset positions implied by theinput-output data are inconsistent with regional net foreign asset positions in the data. The UnitedStates, for example, which has a trade deficit, has a negative net foreign asset position in the databut a positive one in the model, and this inconsistency worsens as the U.S. trade deficit rises be-tween the 1995 and 2011 benchmark calibrations. More research is needed to understand the linkbetween diverging trade balances and international portfolio diversification.

6. Concluding remarks

Between 1995 and 2011, international portfolio diversification increased dramatically in theUnited States and other advanced economies but rose little or fell in the rest of the world. In thispaper I showed that the global structure of production and absorption plays an important role inexplaining this pattern.

First, I used a theoretical model to highlight the roles of country size, trade openness, and tradein intermediate inputs in determining equilibrium country portfolios. This analysis integrated andgeneralized the findings of Baxter and Jermann (1997) and Heathcote and Perri (2013) about theeffects of country size and international trade on international portfolio diversification. For ad-vanced economies, which shrank and became more open to international trade, the theory predictsan increase in diversification. For emerging economies and the rest of the world, growth in sizeand trade openness have opposing effects on diversification in theory. Put together, these predic-tions explain the asymmetry in portfolio diversification growth between advanced and emergingeconomies shown in figure 1a. I also use the theoretical model to derive novel results about theinteraction between country size and trade openness and the role of intermediate input trade indetermining international portfolio diversification. These results, too, are consistent with the dataand provide useful context for my quantitative findings.

Second, I calibrated a more general version of the model to real and counterfactual input-outputdata to assess the quantitative effects of changes in the global production structure on internationalportfolio diversification. To solve for equilibrium portfolios numerically I extended the method ofDevereux and Sutherland (2011) a multi-country environment. This technical contribution shouldprove useful in portfolio choice problems in international macroeconomics as well as other fields.The results of the quantitative analysis indicated that overall change in the global production struc-ture accounts for a large fraction of advanced economies’ growth in portfolio diversification andexplains why diversification in the rest of the world grew little. The counterfactual exercises in-dicated that changes in country size increased advanced economies’ diversification and decreaseddiversification elsewhere, increased trade opennness raised diversification around the world, andincreased intermediate input trade had little impact.

22

It is important to note that changes in the global production structure do not explain all of theobserved growth in international portfolio diversification. For the United States in particular, mymodel leaves 80 percent of the growth in diversification unaccounted for. This is due in part tothe fact that the United States’ place in the global production structure changed less than otherregions’ places. The ADV, EME, and ROW regions changed more in both size and openness totrade, and the benchmark analysis accounts for more of their observed portfolio diversificationgrowth. It is also due, though, to the fact that the only aspect of my calibration that changes be-tween 1995 and 2011 is the global production structure. Further research is needed to assess theimportance of other forces that affect portfolio diversification, especially for the United States.Technological progress that improves investors’ access to information (Mondria and Wu, 2010;Dziuda and Mondria, 2012) and institutional or regulatory changes that facilitate cross-border eq-uity trade are likely candidates. Another promising avenue of investigation is the rise of U.S.-basedmultinational corporations — foreign direct investment undertaken by these entities accounts fora large fraction of the United States’ foreign assets. For emerging economies and the rest of theworld, whose international portfolio diversification has not grown, institutional problems and lackof financial development are likely culprits (Mukherjee, 2015).

Acknowledgements

I thank Fabrizio Perri, seminar participants at the University of Calgary and the Universityof Notre Dame, and two anonymous referees for helpful comments. I would also like to thankthe editor, Matthias Doepke, for his guidance. I acknowledge the Connaught Fund for financialsupport.

Appendix A. Supplementary material

Supplementary material related to this article can be found online at https://www.economics.utoronto.ca/steinberg/files/portfolios_supplement_14dec2017.zip.

References

Arkolakis, C., Ramanarayanan, A., 2009. Vertical Specialization and International Business Cycle Synchronization.Scandinavian Journal of Economics 111 (4), 655–680.

Atalay, E., 2017. How important are sectoral shocks? Working paper, University of Wisconsin.Bacharach, M., 1965. Estimating nonnegative matrices from marginal data. International Economic Review 6 (3), pp.

294–310.Backus, D. K., Kehoe, P. J., Kydland, F. E., 1994. Dynamics of the trade balance and the terms of trade: The j-curve?

American Economic Review 84 (1), 84–103.Backus, D. K., Kehoe, P. J., Kydland, F. E., 1995. International business cycles: Theory and evidence. In: Cooley, T.

(Ed.), Frontiers of Business Cycle Research. Princeton University Press, pp. 331–365.Bai, Y., Zhang, J., 2010. Solving the Feldstein-Horioka Puzzle With Financial Frictions. Econometrica 78 (2), 603–

632.Baqaee, D. R., Farhi, E., 2017. The macroeconomic impact of microeconomic shocks: Beyond hulten’s theorem.

Working Paper 23145, National Bureau of Economic Research,.Baxter, M., Jermann, U. J., 1997. The International Diversification Puzzle Is Worse Than You Think. American

Economic Review 87 (1), 170–80.

23

Bems, R., Johnson, R. C., Yi, K.-M., 2010. Demand Spillovers and the Collapse of Trade in the Global Recession.IMF Economic Review 58 (2), 295–326.

Bems, R., Johnson, R. C., Yi, K.-M., 2011. Vertical Linkages and the Collapse of Global Trade. American EconomicReview 101 (3), 308–12.

Bems, R., Johnson, R. C., Yi, K.-M., 2013. The Great Trade Collapse. Annual Review of Economics 5 (1), 375–400.Coeurdacier, N., 2009. Do trade costs in goods market lead to home bias in equities? Journal of International Eco-

nomics 77 (1), 86–100.Coeurdacier, N., Rey, H., 2013. Home Bias in Open Economy Financial Macroeconomics. Journal of Economic

Literature 51 (1), 63–115.Devereux, M. B., Sutherland, A., 2011. Country portfolios in open economy macro models. Journal of the European

Economic Association 9 (2), 337–369.Dziuda, W., Mondria, J., 2012. Asymmetric Information, Portfolio Managers, and Home Bias. Review of Financial

Studies 25 (7), 2109–2154.Engel, C., Matsumoto, A., 2009. The International Diversification Puzzle When Goods Prices Are Sticky: It’s Really

about Exchange-Rate Hedging, Not Equity Portfolios. American Economic Journal: Macroeconomics 1 (2), 155–88.

Heathcote, J., Perri, F., 2004. Financial Globalization and Real Regionalization. Journal of Economic Theory 119 (1),207 – 243.

Heathcote, J., Perri, F., 2013. The International Diversification Puzzle Is Not as Bad as You Think. Journal of PoliticalEconomy 121 (6), 1108 – 1159.

Hnatkovska, V., 2010. Home bias and high turnover: Dynamic portfolio choice with incomplete markets. Journal ofInternational Economics 80 (1), 113–128.

Hummels, D., Ishii, J., Yi, K.-M., 2001. The nature and growth of vertical specialization in world trade. Journal ofInternational Economics 54 (1), 75–96.

Johnson, R. C., 2014a. Five facts about value-added exports and implications for macroeconomics and trade research.Journal of Economic Perspectives 28 (2), 119–42.

Johnson, R. C., 2014b. Trade in Intermediate Inputs and Business Cycle Comovement. American Economic Journal:Macroeconomics 6 (4), 39–83.

Johnson, R. C., Noguera, G., 2016. A portrait of trade in value added over four decades. Working Paper 22974,National Bureau of Economic Research,.

Kehoe, T. J., Ruhl, K. J., Steinberg, J. B., Forthcoming. Global imbalances and structural change in the united states.Journal of Political Economy.

Koopman, R., Wang, Z., Wei, S.-J., 2014. Tracing Value-Added and Double Counting in Gross Exports. AmericanEconomic Review 104 (2), 459–94.

Lane, P. R., Milesi-Ferretti, G. M., 2007. The external wealth of nations mark II: Revised and extended estimates offoreign assets and liabilities, 1970-2004. Journal of International Economics 73 (2), 223–250.

Lewis, K. K., 1999. Trying to explain home bias in equities and consumption. Journal of Economic Literature 37 (2),pp. 571–608.

Mondria, J., Wu, T., 2010. The puzzling evolution of the home bias, information processing and financial openness.Journal of Economic Dynamics and Control 34 (5), 875–896.

Mukherjee, R., 2015. Institutions, Corporate Governance and Capital Flows. Journal of International Economics96 (2), 338–359.

Obstfeld, M., Rogoff, K., 2001. The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?In: NBER Macroeconomics Annual 2000, Volume 15. NBER Chapters. National Bureau of Economic Research,pp. 339–412.

Perri, F., Quadrini, V., 2011. International recessions. Staff Report 463, Federal Reserve Bank of Minneapolis,.URL https://ideas.repec.org/p/fip/fedmsr/463.html

Tille, C., van Wincoop, E., 2010. International capital flows. Journal of International Economics 80 (2), 157–175.Timmer, M. P., Dietzenbacher, E., Los, B., Stehrer, R., de Vries, G. J., 2015. An illustrated user guide to the world

input-output database: the case of global automotive production. Review of International Economics 23 (3), 575–605.

24

van Wincoop, E., Warnock, F. E., 2010. Can trade costs in goods explain home bias in assets? Journal of InternationalMoney and Finance 29 (6), 1108–1123.

Wang, Z., Wei, S.-J., Zhu, K., 2013. Quantifying International Production Sharing at the Bilateral and Sector Levels.Working Paper 19677, National Bureau of Economic Research,.

25

1995 1999 2003 2007 201110

20

30

40

50

60

70

80USAADVEMEROW

(a) Gross foreign assets (pct. country wealth)

1995 1999 2003 2007 201110

15

20

25

30

35

40

45

50

55USAADVEMEROW

(b) Share of world GDP (pct.)

1995 1999 2003 2007 20114

6

8

10

12

14USAADVEMEROW

(c) Imports + exports (pct. world GDP)

1995 1999 2003 2007 201156

58

60

62

64

66

68

70

72

74

USAADVEMEROW

(d) Intermediate trade (pct. total trade)

Figure 1: Changes in international portfolio diversification and the global production structure

26

Table 1: WIOD regional aggregation

Region Name Countries

1 USA USA2 ADV Australia, Austria, Belgium, Canada, Denmark, Finland, France, Ger-

many, Greece, Japan, Ireland, Italy, Luxembourg, Netherlands, Portu-gal, Sweden, Spain, U.K.

3 EME Brazil, Bulgaria, China, Cyprus, Czech Republic, Estonia, Hungary,India, Indonesia, Korea, Latvia, Lithuania, Malta, Mexico, Poland, Ro-mania, Russia, Slovakia, Slovenia, Taiwan, Turkey

4 ROW Rest of the world

Table 2: Parameters fixed across calibrations

Parameter Value

β 0.96η 0.05ζ 1.00ρ 1.00δ 0.06α 0.36γ 1.00ϕ 1.00τ

[−0.0000004 0.0000011 −0.0000046 −0.0000021

]

P

0.69 −0.02 −0.10 0.000.28 0.79 −0.05 0.03−0.21 0.21 0.59 0.100.23 −0.10 −0.10 0.63

Σ

0.00014 0.00007 0.00003 0.000080.00007 0.00016 0.00005 0.000050.00003 0.00005 0.00045 0.000130.00008 0.00005 0.00013 0.00044

27

Table 3: Input-output representation of model and benchmark input-output tables

Intermediate inputs Final demand

USA ADV EME ROW USA ADV EME ROW GO

(a) Input-output representation of model steady stateUSA m11 m21 m31 m41 c11 + x11 c21 + x21 c31 + x31 c41 + x41 y1

ADV m12 m22 m32 m42 c12 + x12 c22 + x22 c32 + x32 c42 + x42 y2

EME m13 m23 m33 m43 c13 + x13 c23 + x23 c33 + x33 c43 + x43 y3

ROW m14 m24 m34 m44 c14 + x14 c24 + x24 c34 + x34 c44 + x44 y4

VA v1 v2 v3 v4 0.00 0.00 0.00 0.00∑4

i=1 vi

GO y1 y2 y3 y4 0.00 0.00 0.00 0.00∑4

i=1 yi

(b) 1995 benchmarkUSA 19.15 0.88 0.35 0.62 24.33 0.52 0.18 0.18 46.21ADV 0.80 41.73 0.79 1.12 0.63 49.06 0.51 0.61 95.24EME 0.30 0.83 12.41 0.31 0.32 0.54 12.35 0.14 27.21ROW 0.41 1.17 0.47 7.91 0.27 0.52 0.15 9.70 20.59VA 25.55 50.63 13.19 10.63 0.00 0.00 0.00 0.00 100.00GO 46.21 95.24 27.21 20.59 0.00 0.00 0.00 0.00 189.25

(c) 2011 benchmarkUSA 15.11 0.91 0.66 0.53 20.71 0.45 0.28 0.21 38.86ADV 0.73 30.84 1.67 1.73 0.45 34.48 0.78 0.78 71.47EME 0.63 1.69 32.58 1.06 0.51 1.02 24.37 0.56 62.42ROW 0.51 1.46 1.66 12.89 0.21 0.61 0.42 14.15 31.91VA 21.89 36.57 25.85 15.70 0.00 0.00 0.00 0.00 100.00GO 38.86 71.47 62.42 31.91 0.00 0.00 0.00 0.00 204.65

Note: in each panel (b)–(c), all entries are normalized so that world GDP equal to 100.

28

Table 4: Counterfactual input-output tables

Intermediate inputs Final demand

USA ADV EME ROW USA ADV EME ROW GO

(a) Counterfactual 1: change in relative sizes onlyUSA 16.17 0.61 0.45 0.72 20.67 0.40 0.23 0.21 39.47ADV 0.68 29.61 0.94 1.18 0.49 34.98 0.60 0.64 69.12EME 0.43 0.99 25.27 0.57 0.42 0.66 24.76 0.25 53.35ROW 0.42 1.00 0.81 12.23 0.31 0.54 0.26 14.60 30.16VA 21.89 36.57 25.85 15.70 0.00 0.00 0.00 0.00 100.00GO 39.59 68.79 53.32 30.40 0.00 0.00 0.00 0.00 192.10

(b) Counterfactual 2: change in openness onlyUSA 18.91 0.62 0.62 0.77 24.20 0.41 0.33 0.23 46.08ADV 0.69 41.02 1.58 1.54 0.48 48.46 1.07 0.84 95.69EME 0.61 1.67 10.42 1.03 0.56 1.10 11.32 0.46 27.17ROW 0.45 1.30 1.40 6.61 0.31 0.67 0.47 9.10 20.31VA 25.55 50.63 13.19 10.63 0.00 0.00 0.00 0.00 100.00GO 46.21 95.24 27.21 20.59 0.00 0.00 0.00 0.00 189.25

(c) Counterfactual 3: change in intermediate trade shares onlyUSA 19.15 0.93 0.37 0.64 24.41 0.46 0.15 0.17 46.29ADV 0.84 41.73 0.85 1.16 0.59 49.23 0.44 0.57 95.41EME 0.32 0.89 12.41 0.32 0.30 0.48 12.46 0.13 27.32ROW 0.42 1.23 0.49 7.91 0.25 0.46 0.13 9.77 20.66VA 25.55 50.63 13.19 10.63 0.00 0.00 0.00 0.00 100.00GO 46.29 95.41 27.32 20.66 0.00 0.00 0.00 0.00 189.67

Note: in each panel (a)–(c), all entries are normalized so that world GDP equal to 100.

29

Table 5: Measures of global production structure in input-output tables

Region World GDP share(percent)

Total trade(percent world GDP)

Intermediate trade(percent total trade)

(a) 1995 benchmarkUSA 25.55 5.45 61.58ADV 50.63 8.90 62.76EME 13.19 4.88 62.55ROW 10.63 5.97 68.63

(b) 2011 benchmarkUSA 21.89 6.07 65.30ADV 36.57 12.29 66.64EME 25.85 10.93 67.34ROW 15.70 9.75 71.40

(c) Counterfactual 1: change in size onlyUSA 21.89 5.38 61.85ADV 36.57 8.94 62.89EME 25.85 6.58 63.42ROW 15.70 7.14 69.24

(d) Counterfactual 2: change in trade openness onlyUSA 25.55 6.07 61.84ADV 50.63 12.29 62.88EME 13.19 10.93 63.51ROW 10.63 9.75 69.56

(e) Counterfactual 3: change in intermediate trade share onlyUSA 25.55 5.45 64.69ADV 50.63 8.90 66.30EME 13.19 4.88 66.51ROW 10.63 5.97 71.49

30

Table 6: Parameters that vary across calibrations

Counterfactuals

Parameter 1995 Benchmark 2011 Benchmark 1. Size 2. Openness 3. Int. trade

Θi

[1.92 3.80 0.99 0.80

] [1.92 3.21 2.27 1.38

] [1.92 3.21 2.27 1.38

] [1.92 3.80 0.99 0.80

] [1.92 3.80 0.99 0.80

]θi

[3.83 1.93 7.41 9.20

] [3.83 2.29 3.24 5.34

] [3.83 2.29 3.24 5.34

] [3.83 1.93 7.41 9.20

] [3.83 1.93 7.41 9.20

]υi

[0.55 0.53 0.48 0.52

] [0.56 0.51 0.41 0.49

] [0.55 0.53 0.48 0.52

] [0.55 0.53 0.48 0.52

] [0.55 0.53 0.48 0.51

]

µi, j

0.93 0.04 0.01 0.020.02 0.94 0.02 0.030.02 0.06 0.89 0.030.06 0.11 0.03 0.79

0.89 0.04 0.04 0.030.03 0.88 0.05 0.040.02 0.05 0.89 0.050.03 0.11 0.07 0.79

0.92 0.03 0.02 0.030.02 0.91 0.03 0.040.02 0.03 0.92 0.030.05 0.08 0.04 0.83

0.92 0.03 0.03 0.020.02 0.91 0.04 0.030.04 0.11 0.74 0.100.08 0.16 0.10 0.66

0.92 0.04 0.02 0.020.02 0.93 0.02 0.030.03 0.06 0.88 0.030.06 0.12 0.03 0.79

ωi,c, j

0.97 0.01 0.01 0.010.01 0.97 0.01 0.010.01 0.03 0.95 0.010.01 0.04 0.01 0.94

0.97 0.01 0.01 0.010.01 0.95 0.02 0.020.01 0.03 0.95 0.020.01 0.05 0.03 0.91

0.96 0.01 0.02 0.010.01 0.96 0.02 0.010.01 0.02 0.97 0.010.01 0.03 0.01 0.95

0.97 0.01 0.02 0.010.01 0.96 0.02 0.010.02 0.06 0.88 0.040.02 0.05 0.03 0.90

0.97 0.01 0.01 0.010.01 0.97 0.01 0.010.01 0.03 0.95 0.010.01 0.04 0.01 0.94

ωi,x, j

0.89 0.07 0.02 0.020.02 0.96 0.01 0.010.02 0.07 0.90 0.010.03 0.12 0.03 0.82

0.88 0.05 0.06 0.010.02 0.92 0.04 0.010.01 0.04 0.93 0.020.02 0.06 0.06 0.85

0.88 0.06 0.03 0.020.02 0.95 0.01 0.010.02 0.04 0.93 0.010.02 0.09 0.03 0.86

0.88 0.06 0.04 0.020.01 0.95 0.02 0.010.04 0.15 0.77 0.030.04 0.17 0.09 0.71

0.90 0.07 0.02 0.020.02 0.97 0.01 0.010.02 0.06 0.91 0.010.03 0.12 0.02 0.83

31

Table 7: Changes in diversification: data, baseline model, and sensitivity analyses

Counterfactuals

Country Data Benchmark 1. Size 2. Openness 3. Int. trade

(a) BaselineUSA 36.72 7.33 3.23 2.49 0.09ADV 36.83 18.66 6.22 6.34 0.48EME 0.93 4.65 -11.36 42.83 0.69ROW 1.01 0.18 -11.14 32.51 0.45

(b) Higher Armington elasticitiesUSA 36.72 2.19 0.20 1.20 0.22ADV 36.83 10.00 0.29 4.35 0.76EME 0.93 6.19 -3.61 34.29 1.32ROW 1.01 0.38 -7.55 32.38 0.92

(c) Lower Armington elasticitiesUSA 36.72 8.30 4.33 2.97 -0.61ADV 36.83 20.87 8.46 6.93 -0.19EME 0.93 2.72 -14.43 45.70 -0.64ROW 1.01 -0.83 -12.47 32.46 -0.55

(d) Higher final Armington elasticityUSA 36.72 8.63 3.24 2.49 1.07ADV 36.83 20.00 6.23 6.35 1.36EME 0.93 6.60 -10.95 42.49 2.39ROW 1.01 1.46 -11.04 32.37 1.73

(e) Higher intermediate Armington elasticityUSA 36.72 6.42 3.46 2.58 -0.90ADV 36.83 17.98 6.67 6.45 -0.42EME 0.93 2.57 -12.36 43.74 -1.06ROW 1.01 -1.15 -11.51 32.62 -0.88

(f) Higher risk aversionUSA 36.72 1.21 0.04 1.09 0.12ADV 36.83 7.11 -0.18 3.26 0.49EME 0.93 5.12 -2.51 28.37 0.75ROW 1.01 1.53 -5.85 27.33 0.52

Notes: all results reported above are in percentage points. In panel (b), both Armington elasticities,ρ and ζ, are set to 1.25. In panel (c), both are set to 0.75. In panel (d), the final Armingtonelasticity, ρ, is set to 1.25 and the intermediate Armington elasticity, ζ, is set to 0.87. In panel (e),ρ is set to 0.75 and ζ is set to 1.14. In panel (f), the risk aversion parameter, γ, is set to 2.

32

Table 8: Changes in diversification: data, baseline model, and more sensitivity analyses

Counterfactuals

Country Data Benchmark 1. Size 2. Openness 3. Int. trade

(a) BaselineUSA 36.72 7.33 3.23 2.49 0.09ADV 36.83 18.66 6.22 6.34 0.48EME 0.93 4.65 -11.36 42.83 0.69ROW 1.01 0.18 -11.14 32.51 0.45

(b) Uncorrelated shocksUSA 36.72 3.83 2.34 1.52 -0.35ADV 36.83 10.80 3.66 2.85 -0.03EME 0.93 0.82 -7.26 20.11 -0.57ROW 1.01 -2.76 -6.13 14.68 -0.82

(c) Cobb-Douglas productionUSA 36.72 7.24 3.25 2.12 0.04ADV 36.83 18.89 7.02 7.57 0.46EME 0.93 3.90 -11.81 44.51 0.68ROW 1.01 1.18 -11.48 35.39 0.66

(d) Uncorrelated shocks + Cobb-DouglasUSA 36.72 3.84 2.25 1.54 -0.41ADV 36.83 9.34 4.17 2.99 -0.14EME 0.93 -0.51 -7.46 20.24 -0.65ROW 1.01 -2.46 -5.87 13.90 -0.69

Notes: all results reported above are in percentage points. In panel (b), I use the independentstochastic processes listed in equation (31). In panel (c), I use the baseline stochastic process andset the elasticity of substitution between value added and intermediate inputs, η, to one. In panel(d), I use the independent stochastic processes and set η to one.

33

Table 9: Changes in bilateral portfolio shares: baseline model

Home\Foreign USA ADV EME ROW

(a) BenchmarkUSA -7.33 3.02 3.66 0.65ADV 3.66 -18.66 9.94 5.05EME -4.33 3.42 -4.65 5.56ROW -9.68 -1.08 10.94 -0.18

(b) Counterfactual 1: changes in size onlyUSA -3.23 -0.74 1.85 2.12ADV -0.79 -6.22 3.42 3.58EME -5.40 -5.49 11.36 -0.47ROW -3.25 -10.17 2.28 11.14

(c) Counterfactual 2: changes in trade openness onlyUSA -2.49 -2.34 3.45 1.38ADV -2.15 -6.34 5.81 2.67EME 18.33 11.22 -42.83 13.28ROW -6.55 21.90 17.16 -32.51

(d) Counterfactual 3: changes in intermediate share share onlyUSA -0.09 0.09 -0.08 0.07ADV 0.22 -0.48 0.23 0.03EME -0.08 0.66 -0.69 0.10ROW -0.73 1.25 -0.07 -0.45

Note: all results reported above are in percentage points.

34

Table 10: Changes in diversification: data and unbalanced-trade calibrations

Counterfactuals

Country Data Benchmark 1. Size 2. Openness 3. Int. trade 4. Imbalances

(a) BaselineUSA 36.72 9.73 3.17 2.51 0.02 3.40ADV 36.83 30.30 6.76 8.16 0.50 11.57EME 0.93 1.94 -12.32 47.87 0.75 -22.62ROW 1.01 -17.72 -14.77 14.32 0.14 -26.68

(b) Uncorrelated shocksUSA 36.72 6.90 2.29 1.71 -0.43 4.96ADV 36.83 22.86 4.15 3.93 -0.28 14.85EME 0.93 -3.82 -8.19 22.84 -0.69 -18.39ROW 1.01 -26.85 -14.15 6.45 -0.80 -23.49

(c) Cobb-Douglas productionUSA 36.72 12.59 3.28 1.79 0.06 5.21ADV 36.83 27.70 7.99 8.95 0.67 7.01EME 0.93 -0.75 -12.91 50.12 0.78 -31.15ROW 1.01 -10.76 -12.67 17.36 0.50 -22.49

(d) Uncorrelated shocks + Cobb-DouglasUSA 36.72 9.77 2.29 1.31 -0.42 6.93ADV 36.83 18.38 5.18 3.45 -0.23 10.60EME 0.93 -7.88 -8.41 22.96 -0.78 -26.90ROW 1.01 -19.04 -10.87 6.09 -0.58 -16.90

Notes: all results reported above are in percentage points. In all panels, I use the unbalanced input-output tables inthe calibration procedure instead of the balanced tables used in the baseline analysis. In panel (a), I use the sameassigned parameters as in the baseline analysis. In panel (b), I use the independent stochastic processes listed inequation (31). In panel (c), I set the elasticity of substitution between value added and intermediate inputs, η, to one.In panel (d), I use the independent stochastic processes and set η to one.

35